How to Calculate Expected Value in Your Head Instantly

In a trading interview, silence is deadly. When an interviewer asks "What is 37 times 43?", they don't just want the number. They want to see you break down the problem efficiently. Here are the tricks to calculate at lightning speed.

1. The "Difference of Squares" Trick

This is the most common trick for multiplying two numbers that are equidistant from a round number.

Example: 37 * 43

• Find the midpoint: 40.
• Notice that 37 = 40 - 3 and 43 = 40 + 3.
• Recall the formula: $(a - b)(a + b) = a^2 - b^2$.
• Calculation: $40^2 - 3^2 = 1600 - 9 = 1591$.

This turns a hard multiplication problem into a simple subtraction problem.

2. Handling Fractions and Odds

In probability questions, you often need to convert odds to percentages. Memorize these fractions:

• 1/6 ≈ 16.7% (Dice rolls)
• 1/7 ≈ 14.3%
• 1/8 = 12.5%
• 1/9 ≈ 11.1%

3. Expected Value (EV) Shortcuts

EV = $\sum P(x) \cdot x$. In many games, you can factor out common terms.

Problem: You roll a die. If it's even, you get the face value. If it's odd, you pay \$1.

EV = (1/6) * [ (2+4+6) - (1+1+1) ]
Wait, simplifying is faster:
Prob of Even = 1/2. Prob of Odd = 1/2.
Avg(Even) = 4. Avg(Odd payment) = -1.
EV = 0.5 * 4 + 0.5 * (-1) = 2 - 0.5 = 1.5.

Practice Makes Perfect

The only way to internalize these is repetition. Use tools like Zetamac or our own practice drill.